Class X Session 2023-24 Question 8

 MATH SAMPLE QUESTION PAPER

Class X Session 2023-24

MATHEMATICS STANDARD (Code No.041) 

Question 8 

In 𝛥 ABC, DE ‖ AB. If AB = a, DE = x, BE = b and EC = c Then x expressed in terms of a, b and c is:

$$\begin{array}{rl}(a)& \frac{ac}{b}\\ (b)& \frac{ac}{b+c}\\ (c)& \frac{ab}{c}\\ (d)& \frac{ab}{b+c}& & \end{array}$$

Explanation : 

$$\begin{array}{rlcr}SinceDE& \Vert ABwecansimilar\mathrm{△}findthelength& & \end{array}$$

Using the properties of basic proportionality theorem we have 

$$\begin{array}{rl}& \mathrm{△}CDE\sim \mathrm{△}CAB\end{array}$$

$$\Rightarrow \frac{CE}{CB}=\frac{DE}{AB}$$

$$OR\frac{CE}{BE+EC}=\frac{DE}{AB}$$

$$\Rightarrow \frac{c}{b+c}=\frac{x}{a}$$

$$ORx=\frac{ac}{b+c}...bycrossmultiplication$$

 

Guess the Option and comment below  👇